LDV Measurements of Wake-Induced Unsteady Flow within a Turbine Rotor Cascade
by
Takayuki Matsunuma and Yasukata Tsutsui
Mechanical Engineering Laboratory
Agency of Industrial Science and Technology
Ministry of International Trade and Industry
1-2 Namiki, Tsukuba, Ibaraki, 305-8564, Japan
ABSTRACT
The unsteady flow field within an annular turbine rotor was investigated experimentally using an LDV system
with emphasis on the influence of turbine stator wake on the rotor flow field. Detailed measurements of timeaveraged and time-dependent distributions of the velocity, the flow angle, and the turbulence intensity were carried
out at design operating conditions. The obtained data was analyzed from the viewpoints of both absolute flame of
reference (stationary coordinate system) and relative flame of reference (rotating coordinate system) by vectorial
addition of the circumferential velocity component of the rotor speed.
Figure 1 shows the time-dependent distributions of the absolute velocity, absolute flow angle, relative velocity,
relative flow angle, and turbulence intensity. The low velocity area caused by the wake behind the stator
periodically affects the flow field around the rotor. These shapes of time-dependent distributions were re-analyzed
as animations for flow visualization to gain a better understanding of the unsteady flow phenomenon in a turbine
rotor.
t=1/58Tr
t=1/58Tr
Stator
Stator
R otor
Stator
Rotor
Rotor
Wake
(a) Absolute Velocity
t=1/32Ts
Stator
(b) Absolute Flow Angle
Single-Stage Turbine
t=1/32Ts
R otor
(c) Relative Velocity
Stator
(d) Relative Flow Angle
t=1/32Ts
Rotor
Stator
(e) Turbulence Intensity
Fig. 1 Time-dependent flow distributions around turbine rotor cascade
R otor
1. INTRODUCTION
The flow field around the blades of a turbine is highly unsteady and complex. One of the major causes of
unsteadiness is the aerodynamic interaction between the turbine stator and the turbine rotor, namely “rotor-stator
interaction”. Boundary layer behavior, loss generation, and heat transfer in turbines are strongly affected by the
rotor-stator interaction. Even though unsteady flow plays an important role in axial flow turbines, turbines are
designed using steady flow calculation methods. Because actual models of the loss generating mechanisms in
unsteady flow do not exist, empirical correlations are used to account for the effect of unsteadiness. Thus more
knowledge of unsteady rotor-stator interaction is essential to increase the performance of turbines (Dring et al,
1982, Sharma et al, 1985, Binder, 1985, Binder et al, 1985,1987, Rao et al, 1992, Bisby et al, 1998, Venable et al,
1998, Kost et al, 2000). Although the experimental verification of the flow field within rotating blades is rather
complicated, Laser Doppler Velocimetry (LDV) can enable non-intrusive measurement of the flow in a turbine
rotor (Zaccaria and Lakshminarayana, 1995).
In this study, the unsteady flow field within an annular turbine rotor was investigated experimentally using an
LDV system. Detailed measurements of the time-averaged and time-dependent distributions of the velocity, the
flow angle, and the turbulence intensity were carried out at design operating conditions. The obtained data was
analyzed from the viewpoints of both absolute (stationary) flame of reference and relative (rotating) flame of
reference. The effect of the turbine stator wake on the flow field inside the rotor passage was clearly captured.
2. EXPERIMENTAL METHOD
2.1 Experimental Facility
Figure 2 shows a cross-section and photograph of the annular turbine wind tunnel we used. This wind tunnel is
an air suction type with low turbulence intensity. The total length of the wind tunnel is approximately 3.5 meters.
The outer and inner annular wall diameters of the test section are 500 mm and 350 mm, respectively. A single-stage
turbine designed using a free vortex method was installed at the test section. The geometries of the stator and rotor
cascades are shown in Fig. 3 and 4. The geometric design of the profiles was carried out in the traditional manner
by superimposing a thickness distribution on a camber line. The specifications of the stator and rotor cascades are
given in Table 1. For the LDV measurements, the stator and rotor cascades were painted with a flat black paint to
reduce surface reflections.
1m
Bellmouth
Screens
Stator
Blower
Blower
Rotor
Test
Section
Fig.2 Annular turbine wind tunnel
Bellmouth
Air
Table 1 Specifications of turbine cascades
Stator
TIP
(a) TIP
(a) TIP
(b) MIDSPAN
(c) HUB
Fig.3 Geometry of
turbine stator
(c) HUB
Fig.4 Geometry of
turbine rotor
TIP
MID HUB
28
31
Blade Number, N
Chord, C mm
69.1
67.6 66.1
58.5
58.5 58.5
Axial Chord, Cax mm
45.0
42.5 40.0
32.3
40.9 48.0
Blade Span, H mm
(b) MIDSPAN
Rotor
MID HUB
75.0
74.0
Blade Pitch, S mm
56.1
47.7 39.3
Aspect Ratio, H/C
1.09
1.10 1.13
Solidity, C/S
1.23
1.42 1.68
1.15
Inlet Flow Angle, α1 deg
0.0
0.0
-16.5 21.8 51.7
Exit Flow Angle, α2 deg
63.9
67.4 71.1
66.9
63.4 58.7
Stagger Angle, ξ deg
49.3
51.0 52.7
55.9
47.6 33.4
0.0
50.7
43.1 35.5
1.26
1.42 1.65
Inner Diameter, Din mm
350
350
Outer Diameter, Dout mm
500
500
Hub/Tip Ratio, Din /Dout
0.7
0.7
Tip Clearance, mm
0.0
1.0
2.2 Experimental Condition
The Reynolds number based on the rotor chord length and rotor exit velocity is Reout =3.8×104 . The wind tunnel
originally had a low residual turbulence intensity with a value of 0.5% at the midspan of the stator inlet. The axial
velocity at the test section was 4.4m/s and rotor speed was 400rpm to attain design operating conditions (design
rotor inlet flow angle). The flow in this experiment was considered to be incompressible because the Mach
numbers based on the exit conditions was very low Mout =0.029.
2.3 Experimental Techniques
Figure 5 shows schematically the various experimental techniques used through out this reseach. Measurements
using a 5-hole pressure probe and hot-wire anemometry have been reported in previous papers (Matsunuma et al,
1998, 1999). The LDV system used was a standard two-color, four beam, two-dimensional measuring system with
a fiber-optic probe (TSI Incorporated).
It consisted of a 4-W argon-ion laser
tuned to the 488 nm (blue) and 514.5
nm (green) lines. The fiber optic probe
was mounted on a three-dimensional
traverse gear which could be
automatically controlled from a
personal computer. The half -angle
between the beams was 4.29 deg. and
the calculated dimensions of the
measurement volume at e-2 intensity
locations were 0.85 mm in length and
0.073 mm in diameter.
DANTEC
Safex fog fluid “Standard” with a mean
diameter of 1.068 µm was used to seed
Fig.5 Schematic drawing of experimental apparatus of the
annular turbine wind tunnel
3-dimensional
Traverse Gear
Wind Tunnel
Fiberoptic
Probe
Glass
LDV
Window
Fig.7 Wind tunnel with LDV setup
Fig.6 LDV measurement locations (midspan)
the flow. The liquid was atomized using a DANTEC Safex fog generator Model 2001. The tracer particles were
introduced into the test section from the wind tunnel inlet.
Figure 6 shows the LDV measurement locations at the blade midspan. Measurements were made at 43 axial
locations from just downstream of the stator to downstream of the rotor, and 32 pitch-wise locations. At each point
10,000 velocity measurements were acquired. An incremental rotary encoder (1800 pulses/revolution) was
attached to the rotor shaft to detect the rotor angler position. One rotor passage was divided into 58 locations
(encoder pulse number 1800 / rotor number 31), which represent different relative positions between the stator and
the rotor. Figure 7 shows a photograph of the wind tunnel with the LDV setup.
Rotor
Section
(a) Absolute Velocity
Rotor
Section
(e) Absolute Flow Angle
(b) Axial Velocity
(f) Velocity Vector
Rotor
Section
Rotor
Section
(c) Tangential Velocity
Rotor
Section
Rotor
Section
(g) Turbulence Intensity
Fig.8 Time-averaged flow distributions (absolute frame of reference)
Fig.9 Time-dependent absolute velocity distributions (absolute frame of reference)
Fig.10 Time-dependent absolute angle distributions (absolute frame of reference)
3. RESULTS AND DISCUSSION
3.1 Absolute Frame of Reference
Figure 8 shows time-averaged absolute flow distributions. The rotor was mounted between the two dotted lines.
As a consequence of the integration procedure from the viewpoints of the absolute coordinate system, the rotor
blades are not visible in these distributions. In the absolute coordinate system, the swirl flow which came out of the
stator cascade decelerates in the rotor cascade.
Figure 9 shows the time-dependent unsteady absolute velocity distributions at 8 different stator-rotor locations.
Measurements were not obtained in the white region close to the rotor due to the shadow of the blade on the optical
laser. The absolute velocity was normalized by the pitch-wise average of the time-averaged absolute velocity at the
farthest point downstream of the rotor (Axial position Z/Cax,rt=1.41). The low-velocity area caused by the wake
behind the stator cascade affected the flow field around the rotor. Figure 10 shows the time-dependent absolute
flow angle distributions. The absolute flow angle around the rotor was also affected by the stator wake.
The pitch-wise distributions of the time-dependent absolute velocity and flow angle at three different axial
positions are shown in Fig. 11 and 12. At the stator exit (Fig. 11a), the velocity deficit due to the stator wake is
clearly identifiable, and there is seldom any effect from the rotor. At the rotor inlet (Fig. 11b), the velocity defect of
the stator wake decreased from the mixing of the mainstream and the wake of the stator blade, and the effect of the
3
3
2.5
2.5
2.5
2
1.5
1
0.5
0
t=1/58Tr
t=8/58Tr
t=15/58Tr
t=22/58Tr
t=30/58Tr
t=37/58Tr
t=44/58Tr
t=51/58Tr
1.5
1
0.5
0
2
1.5
1
0.5
0
Pitchwise Distance x/S,st
(a) Stator exit (z/Cax,rt=-052)
2
t=1/58T r
t=8/58T r
t=15/58T r
t=22/58T r
t=30/58T r
t=37/58T r
t=44/58T r
t=51/58T r
Absolute Velocity
3
Absolute Velocity
Absolute Velocity
rotor increased. Downstream of the rotor (Fig. 11c), the periodic fluctuation of the absolute velocity due to the
stator wake was about 20% of mean velocity. The rotor induces 38 deg of the periodic fluctuation of the absolute
1.5
1
0.5
0
2
1.5
1
0.5
0
Pitchwise Distance x/S,st
(b) Rotor inlet (z/Cax,rt=-0.14)
2
t= 1/58T r
t= 8/58T r
t= 15/58T r
t= 22/58T r
t= 30/58T r
t= 37/58T r
t= 44/58T r
t= 51/58T r
2
1.5
1
0.5
0
Pitchwise Distance x/S,st
(c) Rotor exit (z/Cax,rt=1.17)
Fig.11 Pitch-wise distributions of time-dependent absolute velocity at stator exit, rotor inlet, rotor exit
-50
-60
-70
-80
2
1.5
1
0.5
0
Pitchwise Distance x/S,st
(a) Stator exit (z/Cax,rt=-052)
-40
-50
10
t=1/58Tr
t=8/58Tr
t=15/58Tr
t=22/58Tr
t=30/58Tr
t=37/58Tr
t=44/58Tr
t=51/58Tr
-60
-70
-80
2
1.5
1
0.5
0
Pitchwise Distance x/S,st
(b) Rotor inlet (z/Cax,rt=-0.14)
Absolute Flow Angle
-40
-30
t=1/58Tr
t=8/58Tr
t=15/58Tr
t=22/58Tr
t=30/58Tr
t=37/58Tr
t=44/58Tr
t=51/58Tr
Absolute Flow Angle
Absolute Flow Angle
-30
0
-10
-20
-30
-40
2
1.5
1
0.5
0
Pitchwise Distance x/S,st
(c) Rotor exit (z/Cax,rt=1.17)
Fig.12 Pitch-wise distributions of time-dependent absolute flow angle at stator exit, rotor inlet, rotor exit
flow angle. The stator also induces 8 deg of angle
fluctuation (Fig. 12c). It was proven that the stator
wake affects the flow downstream of rotor.
3.2 Relative Frame of Reference
Figure 13 explains the velocity triangles that
indicate the correlation between the absolute flow and
relative flow. The absolute and relative flows are
illustrated by blue and red vectors, respectively. The
flow inside the rotor passage in the relative frame of
reference can be analyzed by adding rotor blade
speed (circumferential velocity component) to the
Fig.13 Velocity triangle
velocity vector measured in the absolute coordinate
(correlation between absolute flow and relative flow)
system.
Figure 14 shows the time-averaged flow around the
turbine rotor cascade. The laminar separation breaks out on the rotor suction surface near the trailing edge of the
cascade.
(a) Relative Velocity
(e) Relative Flow Angle
(b) Axial Velocity
(f) Velocity Vector
(c) Tangential Velocity
(g) Turbulence Intensity
Fig.14 Time-averaged flow distributions (relative frame of reference)
Fig.15 Time-dependent distributions of relative velocity (relative frame of reference)
Fig.16 Time-dependent distributions of relative flow angle (relative frame of reference)
Fig.17 Time-dependent distributions of turbulence intensity (relative frame of reference)
Figures 15, 16, and 17 show time-dependent distributions of the relative velocity, the relative flow angle, and the
turbulence intensity, at 8 different stator-rotor locations. The relative velocity and turbulence intensity were
normalized by the pitch-wise average of the time-averaged relative velocity at the point farthest downstream of the
rotor (Z/Cax,rt=1.41). The stator blades move from top to bottom, observed from the relative coordinate system that
rotates with the rotor blades.
The relative velocity and flow angle around the rotor were influenced by the rotor-stator interaction. The width of
the rotor wake changes periodically due to the influence of the stator wake, as shown in Fig. 15.
The high-turbulence intensity region which corresponds to the wake can be clearly observed in Fig. 17. The
straight lines of high-turbulence intensity caused by the stator wake were distorted when they pass through the rotor
passage. This occurs because the flow region near the rotor suction surface moves faster than the flow near the
rotor pressure surface. At the rotor exit, complex unsteady distributions of high-turbulence intensity are formed by
the coalescence of the stator and rotor wakes. .
Figure 18 shows pitch-wise distributions of time-dependent relative velocity, relative flow angle, and turbulence
intensity at rotor inlet. The profiles of the relative velocity and relative flow angle presented in Fig.18(a) and (b)
show that the rotor leading edge had a significant effect on the flow field even at 14 percent of the rotor axial chord
upstream, with the change in velocity and flow angle a 0.2 (40% of mean velocity) and 30 deg, respectively. The
periodic changes due to the stator wake were approximately 0.1 (20%) of the relative velocity and 15 deg of the
relative flow angle.
Pitch-wise distributions of the time-dependent flow at the rotor exit are shown in Fig. 19. The fluctuation of the
velocity deficit along the suction surface was larger than that of the pressure surface side, because the flow
separation on the suction surface near the trailing edge was strongly influenced by the stator wake.
0.6
0.4
0.2
0
2
1.5
1
0.5
0
Pitchwise Distance x/S,rt
(a) Relative velocity
0.2
Turbulence Intensity
10
Relative Flow Angle
Relative Velocity
0.8
0
-10
-20
0.15
0.1
0.05
-30
0
2
1.5
1
0.5
0
2
1.5
1
0.5
0
Pitchwise Distance x/S,rt
Pitchwise Distance x/S,rt
(b) Relative flow angle
(c) Turbulence intensity
Fig.18 Pitch-wise distributions of time-dependent relative flow at rotor inlet (z/Cax,rt =-0.14)
1
0.8
0.6
t=1/32 Ts
t=5/32 Ts
t=9/32 Ts
t=13/3 2Ts
t=17/3 2Ts
t=21/3 2Ts
t=25/3 2Ts
t=29/3 2Ts
0.4
0.2
0
2
1.5
1
0.5
0
Pitchwise Distance x/S,rt
0.2
Turbulence Intensity
70
Relative Flow Angle
Relative Velocity
1.2
65
0.15
60
55
50
0.1
0.05
2
1.5
1
0.5
0
Pitchwise Distance x/S,rt
0
2
1.5
1
0.5
0
Pitchwise Distance x/S,rt
(a) Relative velocity
(b) Relative flow angle
(c) Turbulence intensity
Fig.19 Pitch-wise distributions of time-dependent relative flow at rotor exit (z/Cax,rt=1.17)
4. CONCLUSIONS
Laser Doppler Velocimetry (LDV) was successfully applied to provide detailed data on steady (time-averaged)
and unsteady (time-dependent) flow field near and within the rotor of an annular single-stage turbine. Data analysis
was performed in both absolute and relative coordinate systems. The effect of the turbine stator wake on the flow
of the turbine rotor, namely the rotor-stator interaction, was examined qualitatively and quantitatively.
ACKNOWLEGMENTS
This work was supported by Grants for Core Research for Evolutional Science and Technology (CREST) from
Japan Science and Technology Corporation.
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